Average speed is always equal to magnitude of average velocity. Is this statement true or false ?

Explanation

To determine whether the statement "Average speed is always equal to the magnitude of average velocity" is true or false, we can analyze the definitions of average speed and average velocity.

### Step-by-Step Solution:

1. **Define Average Speed**:
- Average speed is defined as the total distance traveled divided by the total time taken.
\[ \text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}} \]

2. **Define Average Velocity**:
- Average velocity is defined as the total displacement divided by the total time taken.
\[ \text{Average Velocity} = \frac{\text{Total Displacement}}{\text{Total Time}} \]

3. **Understand Distance vs. Displacement**:
- Distance is the total path length traveled, while displacement is the straight-line distance from the initial position to the final position, taking direction into account.
- It is important to note that distance is always greater than or equal to displacement. This means:
\[ \text{Total Distance} \geq \text{Total Displacement} \]

4. **Compare Average Speed and Average Velocity**:
- Since average speed is based on total distance and average velocity is based on total displacement, we can conclude:
\[ \text{Average Speed} \geq \text{Average Velocity} \]
- This implies that the average speed is always greater than or equal to the magnitude of average velocity (since average velocity can be negative depending on direction, but we are considering its magnitude).

5. **Conclusion**:
- Therefore, the statement "Average speed is always equal to the magnitude of average velocity" is **false**. Average speed can be greater than average velocity, but they are not always equal.

### Final Answer:
The statement is **false**.

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